The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X 1 1 1 1 1 1 0 1 1 X X 0 1 1 1 1 X X X 1 1 X X X 1 0 X 2X 0 2X^2+X 2X 0 2X^2+X 2X X^2 2X^2+X 2X X^2+2X 0 2X^2+X X^2+X X^2+2X X^2 2X 0 2X^2+X X^2+X 0 2X X^2+2X X 0 X^2+2X 2X^2 2X^2+X 2X^2+2X X 2X 2X^2 X 2X^2+2X 0 2X^2 2X 2X^2+2X 2X^2 0 X^2+2X 2X^2+X 2X 2X^2 X^2+2X X^2 2X X^2+2X X^2 X 2X^2 X^2+2X 2X^2+X 2X X X^2 X^2+X 2X 2X^2+2X 2X^2+X 2X 2X^2+X 2X^2+X X 2X 2X^2+X 2X^2+X 0 0 0 X^2 0 0 0 0 2X^2 X^2 0 X^2 2X^2 2X^2 0 0 X^2 0 0 X^2 2X^2 2X^2 X^2 X^2 2X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 2X^2 X^2 2X^2 0 X^2 2X^2 X^2 0 X^2 2X^2 0 2X^2 2X^2 0 0 2X^2 2X^2 0 X^2 0 0 2X^2 2X^2 2X^2 2X^2 0 X^2 0 0 2X^2 X^2 X^2 0 0 X^2 2X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 2X^2 0 X^2 2X^2 X^2 X^2 X^2 X^2 2X^2 X^2 2X^2 X^2 X^2 0 2X^2 2X^2 0 X^2 2X^2 X^2 X^2 0 2X^2 0 0 0 X^2 X^2 X^2 0 2X^2 X^2 2X^2 X^2 0 X^2 2X^2 0 2X^2 X^2 0 0 2X^2 2X^2 X^2 X^2 0 X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2 0 X^2 2X^2 X^2 0 X^2 0 0 0 0 0 2X^2 0 X^2 2X^2 X^2 X^2 0 X^2 2X^2 0 2X^2 0 2X^2 0 2X^2 2X^2 0 0 2X^2 X^2 0 0 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2 2X^2 0 X^2 0 0 X^2 0 2X^2 2X^2 2X^2 2X^2 0 2X^2 X^2 2X^2 0 0 0 X^2 0 X^2 2X^2 0 X^2 0 2X^2 2X^2 X^2 0 2X^2 0 X^2 2X^2 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 2X^2 X^2 0 0 X^2 X^2 2X^2 2X^2 X^2 X^2 0 2X^2 0 0 2X^2 X^2 2X^2 X^2 X^2 X^2 0 X^2 0 2X^2 0 X^2 2X^2 X^2 0 X^2 X^2 2X^2 0 X^2 2X^2 X^2 2X^2 0 0 2X^2 0 2X^2 X^2 0 0 X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2 2X^2 0 2X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2 2X^2 generates a code of length 70 over Z3[X]/(X^3) who´s minimum homogenous weight is 126. Homogenous weight enumerator: w(x)=1x^0+32x^126+120x^128+202x^129+450x^131+360x^132+852x^134+720x^135+486x^136+1650x^137+1590x^138+1944x^139+2400x^140+1998x^141+1944x^142+1866x^143+1136x^144+1062x^146+204x^147+228x^149+148x^150+90x^152+64x^153+30x^155+40x^156+22x^159+14x^162+14x^165+10x^168+4x^171+2x^174 The gray image is a linear code over GF(3) with n=630, k=9 and d=378. This code was found by Heurico 1.16 in 2.57 seconds.